jmc

There are ten ways for Tina to select a pair of numbers. The sums 9, 8, 4, and 3 can be obtained in just one way, and the sums 7, 6, and 5 can each be obtained in two ways. The probability for each of Sergio's choices is $1/10$. Considering his selections in decreasing order, the total probability of Sergio's choice being greater is $$\begin{array}{rl}& \left(\frac{1}{10}\right)\left(1+\frac{9}{10}+\frac{8}{10}+\frac{6}{10}+\frac{4}{10}+\frac{2}{10}+\frac{1}{10}+0+0+0\right)\\ & =\boxed{\frac{2}{5}}.\end{array}$$